Question

use a t - test to test the claim about the population mean μ at the given level of significance α using the given samp statistics. assume the population is normally distributed. claim: μ≥7900; α = 0.10 sample statistics: (overline{x}=7600), s = 440, n = 20 (h_{a}:mu = 7900) (h_{a}:mu>7900) c. (h_{0}:mu = 7900) (h_{a}:mu
eq7900) d. (h_{0}:mugeq7900) (h_{a}:mu<7900) what is the value of the standardized test statistic? the standardized test statistic is - 3.05. (round to two decimal places as needed.) what is the p - value? p = 0.003 (round to three decimal places as needed.) decide whether to reject or fail to reject the null hypothesis. choose the correct answer below. a. fail to reject (h_{0}). at the 10% level of significance, there is not enough evidence to reject the claim. b. fail to reject (h_{0}). at the 10% level of significance, there is enough evidence to reject the claim. c. reject (h_{0}). at the 10% level of significance, there is enough evidence to reject the claim. d. reject (h_{0}). at the 10% level of significance, there is not enough evidence to reject the claim.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\leq\alpha\), reject \(H_0\). If \(P - value>\alpha\), fail to reject \(H_0\). Here, \(\alpha = 0.10\) and \(P=0.003\).

Step2: Compare the P - value and \(\alpha\)

Since \(0.003<0.10\) (i.e., \(P - value\leq\alpha\)), we reject the null hypothesis \(H_0\).

Answer:

C. Reject \(H_0\). At the \(10\%\) level of significance, there is enough evidence to reject the claim.